## What is Resistivity?

## Table of Contents

### The Resistivity of Different Materials

Material | Resistivity ρ (ohm.m) |

Silver | 1.59×10^{-8} |

Copper | 1.68×10^{-8} |

Coppe, Annealed | 1.72×10^{-8} |

Aluminium | 2.65 x10^{-8} |

Tungsten | 5.6×10^{-8} |

Iron | 9.71×10^{-8} |

Platinum | 10.6×10^{-8} |

Manganin | 48.2 x10^{-8} |

Lead | 22×10^{-8} |

Mercury | 98×10^{-8} |

Nichrome (Ni.Fe.Cr) | 100 x10^{-8} |

Constantan | 49×10^{-8} |

Carbon* (graphite) | 3-60×10^{-5} |

Germanium* | 1-500×10^{-3} |

Silicon* | 0.1-60 |

Glass | 1-10000×10^{9} |

Quartz (fused) | 7.5×10^{17} |

Hard rubber | 1-100×10^{13} |

### Resistivity Formula

At constant temperature:

- Resistance is directly proportional to length.
- Resistance is inversely proportional to area.

R ∝ L

R ∝ 1/A

R ∝ L/A

R ∝ ρ L/A or ρ = RA/L

**Unit:** ρ = RA/L = Ω-m^{2}/m = Ω.m

### Resistivity Unit

The unit of resistivity is:

CGS unit | Ω.cm |

SI unit | Ω.m |

Dimension of resistivity | M^{1}L^{3}T^{-3}A^{-2} |

## Difference Between Resistance and Resistivity

Resistance is the characteristics of a particular wire where as resistivity is the property of the material of the wire.

Resistance | Resistivity |

Resistance is the property of a material that opposes the flow of electric current through it | Resistivity is the inherent property of a material that describes how strongly it resists the flow of electric current |

Represented by the letter R and its unit of measurement is ohms (Ω) | It is represented by the Greek letter ρ (rho) and its unit of measurement is ohm-meters (Ω·m) |

Resistance depends on the dimensions and shape of the conductor, as well as its temperature and the type of material it is made of | Resistivity is an intrinsic property of a material that does not depend on its dimensions or shape |

The formula for calculating resistance is R = V/I, where V is voltage and I is current | The formula for calculating resistivity is ρ = RA/L, where R is resistance, A is the cross-sectional area of the conductor, and L is its length |

Resistance is a scalar quantity | Resistivity is a tensor quantity |

**Related material:**

- Electric Current
- Ohm’s Law | Ohmic & Non-Ohmic
- Electric Force vs Gravitational Force
- Applications of Electrostatics
- Geometrical Optics Full Chapter MCQs

## Resistivity Dependence on Temperature

**The resistivity ‘ρ’ of a material depends upon its temperature.**

Resistance of material is due to the collision of free electrons with atoms of lattice. As temperature rises collisions increase and hence resistance also increases.

Experimentally it is found that the change of resistance of a wire is nearly linear over a wide range of temperatures above and below 0^{o}C.

### Proof

α = (R_{t }– R_{o})/(R_{o}t)

Let,

- R
_{o}= Resistance of conductor at 0^{o}C - R
_{t}= Resistance of conductor at t^{o}C - R
_{t }– R_{o}= Change in resistance - t = Rise in temperature

Experimentally, It is found that

R_{t }– R_{o} ∝ R_{o}

R_{t }– R_{o} ∝ t

R_{t }– R_{o} ∝ R_{o}t

R_{t }– R_{o} = ∝R_{o}t

∝ = (R_{t }– R_{o})/(R_{o}t)

Where ∝ are the temperature coefficient of resistivity and its unit is k^{-1}.

Using R = (ρL/A) we can prove that:

**∝ = (ρ _{t} – ρ_{o})/( ρ_{o}t)**

- Positive temperature co-efficient: If the value of resistance increases with the rise in temperature then α is positive.
- Negative temperature co-efficient: If the value of resistance decreases with a rise in temperature then α is negative.
**Example:**Germanium & Silicon.

## Conductance

Conductance = 1/Resistance

Also, σ = 1/ρ ; Conductivity = 1/Resistivity

**Unit:** SI-unit of conductivity is:

1/(ohm.m) = ohm^{-1}.m^{-1} = mho.m^{-1}